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1.
2.
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory.
We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary
small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective
system ?(
n
) of observables “up to n loops”, where ?(0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the
quantum action principle and compare it with the usual formulation in terms of Green's functions.
Received: 9 February 2000 / Accepted: 21 March 2000 相似文献
3.
Eric Zaslow 《Communications in Mathematical Physics》1993,156(2):301-331
We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP
1 by the dihedral groupD
4, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP
1 orbifolds. We then considerCP
2/D
4, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Supported in part by Fannie and John Hertz Foundation 相似文献
4.
We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we
present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum
charges is shown to decay as 1/r
6 at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann
statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities,
from orderh
4 on, also decay as 1/r
6. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual
many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally,
we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions.
The particle correlations are found to decay as 1/r
6, while the charge correlation decays faster, as 1/r
10. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises
from the quantum fluctuations of partially screened dipolar interactions. 相似文献
5.
I. Kim G. Mahler 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(3):401-408
In the classical limit no work is needed to couple a
system to a bath with sufficiently weak coupling strength (or
with arbitrarily finite coupling strength for a linear system) at
the same temperature. In the quantum domain this may be expected to
change due to system-bath entanglement. Here we show analytically
that the work needed to couple a single linear oscillator with
finite strength to a bath cannot be less than the work obtainable
from the oscillator when it decouples from the bath. Therefore, the
quantum second law holds for an arbitrary temperature. This is a
generalization of the previous results for zero temperature
[Ford and O'Connell, Phys. Rev. Lett. 96, 020402 (2006); Kim and Mahler, Eur. Phys. J. B 54, 405 (2006)]; in the high temperature limit we recover the
classical behavior. 相似文献
6.
F. Jeske Th. Stöferle M. DeKieviet 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2011,63(1):25-32
In this paper we present an experiment performed with an atomic beam spin echo
interferometer, in which massive intraparticle entanglement is demonstrated. In the
longitudinal Stern-Gerlach arrangement the nuclear spin and linear momentum of
3He particles are inextricably linked, such that the overall system state
cannot be written as the tensor product of the corresponding Hilbert spaces. The measured
data show maximal entanglement between ℋ
I
and ℋ
p
. This hybrid system of one quantum and one classical
degree of freedom is a textbook example of entanglement between discrete and continuous
observables. 相似文献
7.
Alastair Brodlie 《International Journal of Theoretical Physics》2003,42(8):1707-1731
p-Mechanics is a consistent physical theory which describes both quantum and classical mechanics simultaneously (V. V. Kisil, p-Mechanics as a physical theory. An Introduction, E-print:arXiv:quant-ph/0212101, 2002; International Journal of Theoretical Physics
41(1), 63–77, 2002). We continue the development of p-mechanics by introducing the concept of states. The set of coherent states we introduce allows us to evaluate classical observables at any point of phase space and simultaneously to evaluate quantum probability amplitudes. The example of the forced harmonic oscillator is used to demonstrate these concepts. 相似文献
8.
Sinem Binicioǧlu M. Ali Can Alexander A. Klyachko Alexander S. Shumovsky 《Foundations of Physics》2007,37(8):1253-1277
Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S.
Shumovsky, J. Phys: Conf. Series
36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification
of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states
with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In
particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration,
we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A
number of physical examples are considered.
相似文献
9.
D. Braun 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(1):3-12
I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation
reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator,
if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical
strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently
many times the formulae become entirely classical, and powerful classical trace formulae apply.
Received 7 October 1999 相似文献
10.
Prot Pakoński Gregor Tanner Karol Życzkowski 《Journal of statistical physics》2003,111(5-6):1331-1352
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L
n
(G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour. 相似文献
11.
No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical
field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical
variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures
ρ on Ω having zero mean value and dispersion σ2(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based
on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ2(ρ) = hn (for n = 2 we obtain the conventional quantum formalism). 相似文献
12.
Howard Barnum Gerardo Ortiz Rolando Somma Lorenza Viola 《International Journal of Theoretical Physics》2005,44(12):2127-2145
We define what it means for a state in a convex cone of states on a space of observables to be generalized-entangled relative to a subspace of the observables, in a general ordered linear spaces framework for operational theories. This extends
the notion of ordinary entanglement in quantum information theory to a much more general framework. Some important special
cases are described, in which the distinguished observables are subspaces of the observables of a quantum system, leading
to results like the identification of generalized unentangled states with Lie-group-theoretic coherent states when the special
observables form an irreducibly represented Lie algebra. Some open problems, including that of generalizing the semigroup
of local operations with classical communication to the convex cones case, are discussed.
PACS: 03.65.Ud. 相似文献
13.
The classical matter fields are sections of a vector bundle E with base manifold M, and the space L
2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of Cb¥(M){C_b^\infty(M)} on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum
context, we show that this module action defines an automorphism group on the algebra of the canonical anticommutation relations,
CAR(L
2(E)), with which we can perform the analogous localization. That is, the net structure of the CAR(L
2(E)) w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction
maps, and as a corollary, we prove a well–known “folk theorem,” that the CAR(L
2(E)) contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E. 相似文献
14.
We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator
excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular
behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in
quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree
of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity
parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability
and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets
in quantum chaos.
Zh. éksp. Teor. Fiz. 113, 111–127 (January 1998) 相似文献
15.
The Courant theorem provides an upper bound for the number of nodal domains of eigenfunctions of a wide class of Laplacian-type
operators. In particular, it holds for generic eigenfunctions of a quantum graph. The theorem stipulates that, after ordering
the eigenvalues as a non decreasing sequence, the number of nodal domains ν
n
of the n
th eigenfunction satisfies n ≥ ν
n
. Here, we provide a new interpretation for the Courant nodal deficiency d
n
= n − ν
n
in the case of quantum graphs. It equals the Morse index — at a critical point — of an energy functional on a suitably defined
space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning — it is the number
of unstable directions in the vicinity of the critical point corresponding to the n
th eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the
corresponding critical partitions are studied in detail. 相似文献
16.
Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition. 相似文献
17.
The symmetrization postulates of quantum mechanics (symmetry for bosons, antisymmetry for fermions) are usually taken to entail
that quantum particles of the same kind (e.g., electrons) are all in exactly the same state and therefore indistinguishable in the strongest possible
sense. These symmetrization postulates possess a general validity that survives the classical limit, and the conclusion seems
therefore unavoidable that even classical particles of the same kind must all be in the same state—in clear conflict with
what we know about classical particles. In this article we analyze the origin of this paradox. We shall argue that in the
classical limit classical particles emerge, as new entities that do not correspond to the “particle indices” defined in quantum mechanics. Put differently, we show
that the quantum mechanical symmetrization postulates do not pertain to particles, as we know them from classical physics, but rather to indices that have a merely formal significance. This conclusion raises
the question of whether many discussions in the literature about the status of identical quantum particles have not been misguided. 相似文献
18.
Derek W. Robinson 《Communications in Mathematical Physics》1967,6(2):151-160
The thermodynamic limit of a quantum spin system is considered. It is demonstrated that for a large class of interactions and a wide range of the thermodynamic parameters the equilibrium state of the system is describable by an extremalZ
v
-invariant state (a single phase state) over aC* algebra of local observables. It is further shown that the equilibrium state may be obtained as the solution of a variational problem involving the mean entropy. These results extend results previously obtained for classical spin systems byGallavotti, Miracle-Sole andRuelle. 相似文献
19.
《Journal of Nonlinear Mathematical Physics》2013,20(1):50-53
Abstract We discuss stationary solutions of the discrete nonlinear Schrödinger equation (DNSE) with a potential of the ? 4 type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that there may arise chaotic spatial structures in the form of incommensurate or irregular quantum states. As a first (typical) example we consider a single electron which is strongly coupled with phonons on a 1D chain of atoms — the (Rashba)–Holstein polaron model. In the adiabatic approximation this system is conventionally described by the DNSE. Another relevant example is that of superconducting states in layered superconductors described by the same DNSE. Amongst many other applications the typical example for a classical lattice is a system of coupled nonlinear oscillators. We present the exact energy spectrum of this model in the strong coupling limit and the corresponding wave function. Using this as a starting point we go on to calculate the wave function for moderate coupling and find that the energy eigenvalue of these structures of the wave function is in exquisite agreement with the exact strong coupling result. This procedure allows us to obtain (numerically) exact solutions of the DNSE directly. When applied to our typical example we find that the wave function of an electron on a deformable lattice (and other quantum or classical discrete systems) may exhibit incommensurate and irregular structures. These states are analogous to the periodic, quasiperiodic and chaotic structures found in classical chaotic dynamics. 相似文献
20.
A P Balachandran 《Pramana》2001,56(2-3):223-237
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators
are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major
axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would
not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with
smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and
with further refinements of the axiom, its C
K - and C
--structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of
only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less
differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating
these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental
issues concerning the role of time in quantum physics are also addressed. 相似文献